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Uncertainty Quantification Analysis for a Ka-band
Deployable Mesh Reflector for INCUS
Alessio Mancini
Flight Communication Systems
Jet Propulsion Laboratory, California
Institute of Technology
Pasadena, CA, USA
alessio.mancini@jpl.nasa.gov
Quinn Kostelecky
Inner Planet Mission Analysis
Jet Propulsion Laboratory, California
Institute of Technology
Pasadena, CA, USA
quinn.kostelecky@jpl.nasa.gov
Paolo Focardi
Flight Communication Systems
Jet Propulsion Laboratory, California
Institute of Technology
Pasadena, CA, USA
paolo.focardi@jpl.nasa.gov
Abstract — This paper presents a statistical analysis to evaluate
the impact of fabrication tolerances of a deployable mesh reflector
on its electromagnetic performance. This study is carried out
assigning a random displacement of the nodes composing the mesh
of the reflector from their ideal position along the parabolic shape.
This analysis is applied to a deployable mesh reflector operating
at Ka-band which is being considered for a new NASA Earth
science mission. The goal of this study is to evaluate how much an
incorrect placement of the nodes will impact the radiation pattern
of the reflector and its pointing.
Keywords — Deployable mesh reflector, Ka-band, uncertainty
analysis, space application.
I. INTRODUCTION
Among the various effects of climate change is the rise of
ocean temperature which produces more severe and intense
storms. Therefore, improving weather models and other tools to
more accurately predict the consequences of climate change and
their impact on the weather is becoming more critical. For this
purpose, NASA selected a new Earth Science mission called
INvestigation of Convective UpdraftS (INCUS) [1]. The goal of
the mission is to study in detail how air and water vapor move
inside tropical storms and thunderstorms and assess their effects
on weather and climate models. To carry out this study, the
mission will use three identical SmallSats, each one equipped
with a Ka-band deployable mesh reflector illuminated by seven
independent and offset feedhorns with partially overlapping
beams. A description of the antenna system of the SmallSat is
provided in [2].
A deployable mesh reflector was proposed for the INCUS
mission to meet the gain requirement while maintaining low
mass and stowed volume during launch. The advantages in
terms of mechanical features obtained with this type of reflector
come at a cost in terms of electromagnetic performance,
especially when employed at higher frequencies. In fact, the
mesh reflector shape is defined by nodes which approximate the
shape of a parabolic surface. In an ideal scenario, the nodes
would be placed in their exact position, however, because of
manufacturing tolerances and thermal variations, an incorrect
placement of these nodes can affect the global performance of
the reflector. Ruze in [3] presents a statistical study on the
degradation of the radiation pattern of a parabolic reflector as a
function of the surface rms error. In [4] and [5], other studies on
this topic have been performed, but they are of deterministic
nature. A summary of the analyses on the surface distortions of
reflectors was provided by Corkish in [6]. More recent studies
on the characterization of surface distortions of deployable
reflectors are presented in [7] and [8]. The statistical study
presented here aims at calculating the changes in
electromagnetic performance of the reflector due to
imperfections in the location of its nodes and determining if the
corresponding radiation pattern still meets the mission
requirements. In Section II a brief description of the INCUS
mission and the multi-beam overlapping concept are provided.
Section III discusses the type of analysis performed on the
deployable mesh reflector.
II. THE INCUS MISSION
A. The Concept
A storm begins to form when air and water vapor rapidly rise
generating towering clouds which are the primary source of
precipitation. Severe storms are more likely to occur when a
large mass of water vapor and air is transported upward in the
vertical atmosphere (Convective Mass Flux - CMF). CMF
dynamics are still not very well understood and its systematic
measurement would provide additional critical knowledge of
this phenomenon. INCUS aims at directly addressing how
convective storms, heavy precipitations, and clouds generate in
tropical regions [2,9].
B. Multi-Beam Overlap Concept
Three satellites (SmallSats) flying along the same orbit will be
used to gather an accurate description of a storm, each one
equipped with an identical antenna system capable of generating
seven partially-overlapping beam tracks. The antenna includes a
deployable mesh reflector of 1.6 m diameter to provide at least
50 dB of gain with seven feed horns. Details about the reflector
antenna geometry and construction are provided in [10]. The
seven beams are required to increase the total field of view of
the radar instrument, while the partial overlap is required for
redundancy and to relax the pointing requirements. The concept
of the INCUS constellation is shown in Figure 1 [11,12]. The
three satellites will fly at an altitude of about 500 km. To provide
the necessary spatial resolution, the antenna feed is made of
seven independent horns that provide seven ground tracks with
2/3 3 dB beam partial overlap in the across track direction. Each
3 dB beam is about 0.35° and produces roughly a 3.1 km
coverage from an altitude of 500 km. The three satellites are
located in the same orbital plane but their respective ground
tracks do not match exactly because of Earth’s rotation and their
tracking time is not simultaneous. INCUS2 and INCUS3 are
delayed with respect to INCUS1 by 30 seconds and 120 seconds,
respectively. In Figure 2, a close-up of each SmallSat is shown
from a Nadir view.
Fig. 1. A pictorial representation of the INCUS constellation composed of the
three SmallSats (INCUS1, INCUS2, and INCUS3). Visualization created using
Satellite Orbit Analysis Program (SOAP) developed by the Aerospace
Corporation .
Fig. 2. The Nadir view showing a closed-up of the three SmallSats identifying
the footprint of the seven partially-overlapping beams sweeping along a
common ground track. Visualization created using Satellite Orbit Analysis
Program (SOAP) developed by the Aerospace Corporation.
The white line presented in Figure 2 represents the target
observation track. INCUS1, INCUS2, and INCUS3 orbits are
denoted by the green, orange, and red lines. In the figure are also
indicated the footprints of the seven beams showing the
feedhorn configuration [2]. During an orbit, the three satellites
slowly roll left and right to keep pointing at the same ground
track. To ensure the correct coverage of the ground track,
pointing accuracy is very important. This is guaranteed only if
the whole antenna system, including the reflector, is stable to
within a preliminary absolute pointing requirement of 0.18°.
C. Antenna System
The antenna system employed for the INCUS mission is the
same for all three spacecrafts and it is composed of a deployable
mesh reflector of 1.6 m and seven identical feed horns. The
preliminary focal length over diameter (f/D) is equal to 0.7 and
the edge offset is 20 cm. The feed horns are arranged in an
optimized “Z” configuration which is a compromise between
coverage and RF performance. We tried to keep the seven horns
as close as possible to the focus of the reflector and at the same
time ensure the required beam overlap in the across track
direction. The antenna operates at 35.75 GHz. The preliminary
performance of the feed horn is presented in [2]. The feed
assembly, the WR28 waveguides feeding it, and their
supporting structure are all made of aluminum. The reflector
has a central hub with composite ribs supporting the mesh
surface. The reflector and the feed are connected to the same
aluminum supporting structure.
III. UNCERTAINTY QUANTIFICATION ANALYSIS
A. Model Description
Given the nature of the mesh reflector, to ensure a high
modeling and pointing accuracy, a rigorous analysis of the
antenna system is necessary. An accurate and complete thermal
model will provide information about how the entire antenna
system will behave on orbit. The movements of the horn
assembly and of its supporting structure, being all made of
aluminum, will be very well described by the thermal model.
The reflector shape is a slightly different story. There is a
nominal reflector shape by design. There are variations due to
manufacturing tolerances between the three spacecrafts and
there are variations due to subsequent deployments during
testing. On top of all that, there are thermal variations once in
orbit. The relationship between all of these variations and the
performance of the RF model are still not very well understood
unfortunately as the thermal variations of an aluminum
structure. Also, operating at Ka-band, small mechanical
differences that at lower frequencies would be negligible, might
play a role. While the ultimate shape of the reflector and the
location of its nodes will be accurately measured later on during
the development of the mission, and used for final RF
performance verification and validation, for now we would like
to get a better understanding of what changes in RF performance
and pointing we should expect based on certain tolerances on the
nodes’ location. Eventually we will reconcile the results of our
model with the measured reflector surface and its as-built
tolerances. To perform all these analyses a recently developed
TICRA tool for Uncertainty Quantification (UQ) [13] was
employed. This new tool performs a statistical analysis that
allows a random displacement of each node within a relative
range of error defined by the user.
In a 3-D coordinate system containing the parabolic
reflector, the x- and y-axes represent the longitudinal axes, and
the z-axis is the latitude. The ideal location of the ith-node that
lays on the parabolic surface, is identified by the point with
coordinate (x0i, y0i, z0i), for i = 1,2,..,n, where n is the total
number of nodes composing the mesh. The statistical algorithm
simulates the manufacturing imprecisions of the nodes by
placing the ith-node at (x0i+Δxi, y0i+Δyi, z0i+Δzi), for i = 1,2,..,n.
Δi is the displacement along a specific coordinate corresponding
to the ith-node. In Figure 3, the model of the deployable mesh
reflector generated by the TICRA tool before applying the UQ
analysis is shown. For this study, an ideal feed horn was
employed to illuminate the reflector instead of the feed horn
developed in [2]. The ideal feed horn irradiates a Gaussian beam
with -12 dB taper on the reflector’s edge. We chose to use a
Gaussian beam for this analysis rather than a more realistic
feedhorn in order to focus our attention on the reflector RF
performance. While in this study the same tolerance was applied
to all the nodes of the reflector, the surface can be divided in
various regions with different tolerances applied to each region.
B. Results
The statistical analysis was executed selecting a normal
distribution to define the nodes displacement error. The
displacement error for this study was chosen to be a
conservative ±1 mm in each one of the three coordinates. We
believe this to be close to a worst-case scenario. The first set of
simulations was conducted by first assuming a displacement
error only on the x- and y-coordinates (no error on the z-
coordinate) of the node. The second analysis executed applied
a node displacement only on the z-coordinate (no error on the x-
and y-coordinates).
Fig. 3. A screenshot of the deployable mesh reflector model with diameter of
1.6 m developed for the UQ analysis illuminated by an ideal Gaussian feed
horn.
Finally, a third set of simulations applied displacement errors
along x-, y-, and z-coordinates. The purpose of performing
separate analysis for the longitudinal coordinates and the
latitude coordinate was to determine which one of them makes
the electromagnetic performance of the reflector more sensitive
to manufacturing imprecision. The results of the statistical
analysis are shown in terms of radiation patterns for the co-
polarized component of the E-field only, on the φ = 0° and 90°
cuts. The analysis provides the 95 percentiles. In each plot four
curves are shown. Two of those indicate the upper and lower
bounds which represent the worst- and best-case scenarios
respectively, and they include 95% of the total cases possible
ranging between ±1 mm tolerance. The other two curves are the
expected value (average) and the nominal case (ideal) plotted for
reference. All radiation patterns are plotted at 35.75 GHz.
1) Tolerance Analysis on the xy-coordinates
The results of the statistical analysis on the nodes’
displacement along the xy-coordinates are presented here and
discussed. In Figure 4, the radiation pattern at φ = 0° is shown.
As expected, the nominal case lies within the upper and lower
bounds. The main variation in performance of the reflector
occurs in the minor side-lobe level (SLL). The gain and closer
SLL are not significantly affected by the nodes’ displacement
along the xy-coordinates. In Figure 5, the radiation pattern at φ
= 90° is shown. In this cut, the grating lobes are noticeable due
to the faceted surface of the mesh reflector. On this plane, the
radiation pattern exhibits similar RF performance in term of
tolerance as in the φ = 0° plane.
Fig. 4. The radiation pattern at 35.75 GHz of the mesh reflector at φ = 0°
showing the results for the tolerance analysis performed on the xy-coordinates.
2) Tolerance Analysis on the z-coordinate
The statistical investigation performed on the nodes’
displacement along the z-coordinate is shown below. In Figure
6, the radiation pattern on the φ = 0° cut is shown. It appears
Fig. 5. The radiation pattern at 35.75 GHz of the mesh reflector at φ = 90°
showing the results for the tolerance analysis performed on the xy-coordinates.
evident that the RF performance of the mesh reflector is more
sensitive to a displacement occurring along the z-axis, as
expected since displacements along the z-axis affect the
aperture phase much more than displacements in the x- and y-
axes. While the peak gain is not critically affected, the sidelobes
rise to higher levels than for the case where the displacement
was along the xy-axes.
Fig. 6. The radiation pattern at 35.75 GHz of the mesh reflector at φ = 0°
showing the results for the tolerance analysis performed on the z-coordinate.
The radiation pattern calculated for this scenario on the φ = 90°
cut is shown in Figure 7. Similar conclusions to the pattern on
the φ = 0° cut can be made.
3) Tolerance Analysis on the xyz-coordinates
The last case analyzed includes variation along all three
coordinates (x, y, and z). This is expected to be the worst-case
scenario. The radiation pattern for φ = 0° is presented in Figure
8. Again, the major impact on the RF performance concerns the
SLL while the peak gain is not appreciably changed. It appears
evident by direct comparison with Figures 4 and 6, that by
introducing a displacement of the nodes in all three directions
the highest sidelobes are generated. This latest case is dominated
by displacement along the z-axis.
Fig. 7. The radiation pattern at 35.75 GHz of the mesh reflector at φ = 90°
showing the results for the tolerance analysis performed on the z-coordinate.
Fig. 8. The radiation pattern at 35.75 GHz of the mesh reflector at φ = 0°
showing the results for the tolerance analysis performed on the xyz-coordinates.
Fig. 9. The radiation pattern at 35.75 GHz of the mesh reflector at φ = 90°
showing the results for the tolerance analysis performed on the xyz-coordinates.
In Figure 9, the radiation pattern is shown for the cut at φ = 90°,
with similar conclusions about those discussed above for Figure
8. It is worth noting that while this analysis provides a very clear
view of changes in the SLL, it appears that the overall pointing
of the antenna is not affected by the tolerances used in this study.
This is not unexpected since a random tolerance distribution was
used and the reflector surface contains many nodal points. The
phase error is expected to average out across the surface, which
would tend to lower gain and raise sidelobes, but not affect
pointing in a significant way.
IV. CONCLUSIONS
A deployable mesh reflector operating at Ka-band is being
proposed for the antenna system for INCUS, a new Earth
Science mission approved by NASA. To ensure that the
requirements for high pointing accuracy of the antenna are met,
imperfections occurring during the manufacturing process of the
mesh reflector should be considered to evaluate their impact on
the RF performance. For this purpose, a statistical tool was used
to evaluate how the nodes’ displacements affect the radiation
pattern of the reflector. Three analysis were carried out to
account for nodes’ displacements: along the xy-axes, along the
z-axis, and on all three coordinates. The scenario where the
displacement occurred in all three coordinates represented the
worst-case scenario and it was dominated by tolerances on the
z-axis. The consequence of nodes’ displacement mainly impacts
the sidelobes while the gain is not considerably affected.
ACKNOWLEDGMENT
This work was carried out at the Jet Propulsion Laboratory,
California Institute of Technology, under a contract with the
National Aeronautics and Space Administration. © 2023
California Institute of Technology. Government sponsorship
acknowledged.
The authors would like to thank TICRA for developing this
new tool and for the continuous technical support provided for
this study.
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